% SMOOTHBRANCH   Smoothen points along one path.
% (scheme package)
%
% [Xs, Ys, Zs] = smoothbranch (X, Y, Z, p, n)
% -------------------------------------------
%
% smoothens a branch given by consecutive (!) 3D coordinates. This changes
% (shortens) the total length of the branch significantly.
%
% Input
% -----
% - X, Y, Z::Nx1 vectors: input coordinates
% - p::0..1: percent smoothing at each iteration step
% - n::integer>0: number of smoothing iterations
%
% Output
% ------
% - Xs, Ys, Zs::Nx1 vectors: Output coordinates
%
%
% Example
% -------
% X = 2*rand(10,1)+(1:10)'; Y = 2*rand(10,1)+(1:10)'; Z = zeros(10,1);
% [Xs Ys Zs] = smoothbranch (X, Y, Z, 0.9, 5);
% clf; hold on; plot3(X, Y, Z, 'k-'); plot3(Xs, Ys, Zs, 'r-');
%
% See also smooth_tree
% Uses
%
% the TREES toolbox: edit, visualize and analyze neuronal trees
% Copyright (C) 2009  Hermann Cuntz

function [Xs Ys Zs] = smoothbranch (X, Y, Z, p, n)

if length (X) > 2,
    for ward = 1 : n,
        X2 = X (2 : end - 1);
        Y2 = Y (2 : end - 1);
        Z2 = Z (2 : end - 1);
        X1 = X (1 : end - 2);
        Y1 = Y (1 : end - 2);
        Z1 = Z (1 : end - 2);
        X3 = X (3 : end);
        Y3 = Y (3 : end);
        Z3 = Z (3 : end);
        u  = ((X2 - X1) .* (X3 - X1) + (Y2 - Y1) .* (Y3 - Y1) + (Z2 - Z1) .* (Z3 - Z1)) ./ ...
            ((X3 - X1).^2 + (Y3 - Y1).^2 + (Z3 - Z1).^2);
        Xu = X1 + u .* (X3 - X1);
        Yu = Y1 + u .* (Y3 - Y1);
        Zu = Z1 + u .* (Z3 - Z1);
        Xs = X2 + p .* (Xu - X2);
        Ys = Y2 + p .* (Yu - Y2);
        Zs = Z2 + p .* (Zu - Z2);
        Xs = [X(1); Xs; X(end)];
        Ys = [Y(1); Ys; Y(end)];
        Zs = [Z(1); Zs; Z(end)];
        X  = Xs;
        Y  = Ys;
        Z  = Zs;
    end
else
    Xs = X;
    Ys = Y;
    Zs = Z;
end
